Prerequisite material

I have produced a worksheet with solutions covering prerequisite mathematics for Security I.
This is a new worksheet and there are likely to be bugs, please report them and make suggestions for improvements.
There may be cake or similar for those who do so.
This is strictly optional, only the probability material is required for the current Security I course, the rest is required for Security II.
The source code is available.

Supervision questions last updated for 2014-2015.

If you write a program to solve any of these exercises I want to see the source code.

In order to communicate securely about supervisions we need a way of authenticating emails.
All electronic submissions should be signed using your GPG key and encrypted to my work key D74933D9.
This is an opportunity to learn to use encryption in a controlled environment so please do this properly we can discuss this at the start of the first supervision.
You should submit an explanation of what you did to create and publish a key with your answers.

Exercises 1-4, 7-9 from Markus's exercise sheet.

Supervision 2 - lectures 5-7: Entity authentication, Access control

Exercises: 20-22, 32, 2004 Paper 3 Question 9,
"Do software updates increase or decrease risk of successful attack?"
and (3.21 from p109 1st Edition or 3.29 from p106 2nd Edition) of "Introduction to Modern Cryptography" by Jonathan Katz and Yehuda Lindell:
Given two encryption schemes one of which is CPA secure (you don't know which) construct a scheme out of them which is CPA secure giving a full proof of your answer.